Sequential kriging‐based closure approximations for flow‐induced fiber orientation and prediction of composite stiffness

Orientation tensor has been widely applied to predict the orientation state of the fibers in injection molding simulations. Unfortunately, calculating the second‐order orientation tensor needs to know the four‐order orientation tensor, thus requiring a closure approximation. Developing an efficient and accurate closure has been a challenging subject. This article develops a sequential Kriging‐based closure (KRI) approximation. We constructed the Kriging approximation of fourth‐order orientation tensor in terms of the second‐order orientation tensor. The maximization of expected improvement adds the second‐order orientation tensors to improve the accuracy of the closure. Results demonstrate that the prediction of the KRI closure to accurately predict fiber orientation and fiber‐reinforced composites stiffness is more accurate than the Hybrid, Orthotropic, and Natural closure for majority of the flows in industrial manufacturing processes. POLYM. COMPOS., 40:1748–1761, 2019. © 2018 Society of Plastics Engineers